Investigation of 8th grade students' visual reasoning skills regarding algebra questions asked in high school entrance examination

The aim of this study is to investigate the visual reasoning skills of 8th grade students regarding algebra questions asked in the Central Common Exams of the High School Transition System (LGS). In this study, since only the 8th grade was considered as the grade level, a single case design was used, and since the visual reasoning skills of middle and high level students were analysed, a nested single case design was used. Criterion sampling, one of the purposeful sampling methods, was used to determine the students in the study group. The study group of this research consists of 18 students selected from the 8th grade students studying in the 2023-2024 academic year in three secondary schools selected among the public schools in the central district of Afyonkarahisar province. A total of six students, three students with medium and high achievement levels, were selected from each school. Thus, the study group consisted of 18 students, six students from each school. The data of the study were collected by using 'Algebra Test' and 'Semi-structured Interview Questions Form' data collection tools prepared by the researcher. The questions used in the Algebra Test consist of 15 questions selected from the questions that include the acquisitions related to the algebra subject area of the mathematics subtest asked in the LGS central common exams between 2018-2023. Algebra Test was applied to 18 students. Using the Semi-Structured Interview Questions Form, interviews were conducted with 6 students selected among 18 students. Data analysis was conducted using 'content analysis'. The data obtained were analysed based on the conceptual framework proposed by Geçici and Türnüklü (2021). In the study, it was determined that the most preferred visual representation type of the participants was drawing representation. However, there are also participants who prefer tabular representation. It was observed that no student used the picture representation. It was determined that students who could use different visual representations could easily complete the steps necessary for mathematical thinking while solving the questions. It was observed that students who could switch between visual representations were more successful. It was observed that students with high achievement levels were more successful than other students in the steps of specialisation, conjecture, verification and generalisation, which are the components of transition to mathematical thinking.